The equation of a circle $C$ is $x^2+y^2-16x+16y+119 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2-16x) + (y^2+16y) = -119$ $(x^2-16x+64) + (y^2+16y+64) = -119 + 64 + 64$ $(x-8)^{2} + (y+8)^{2} = 9 = 3^2$ Thus, $(h, k) = (8, -8)$ and $r = 3$.